Captain Falcon
I'm pretty sure everyone has decent experience in this matchup due to Falcon's popularity. I play a lot against one of the best Falcons in AZ, and handily won against a Falcon in pools last week.
Pros
Really predictable recovery, easy to gimp
We can crouch to avoid a lot of his attacks
He's combo fodder since he's heavy and falls fast
Cons
Tons of KO power and we're already light
Much faster than us on the ground and in the air
Copy Ability
In casual play, this is a god-tier move to style on your opponents. In competitive play, this move is god-awful. If you ever swallow Falcon, get rid of this ability ASAP as your neutral b will almost always be better.
Custom Moves
Jumping Inhale - just adding another tool to Kirby's list of moves that can gimp Falcon for an early kill
Hammer Bash - charging a hammer can result in a huge punish due to Falcon's speed and power
Upper Cutter - it's a kill move, it makes it very difficult for Falcon to spike you offstage, and it's great at stage-spiking Falcon's recovery
Stone(?) - this is pretty much personal preference, although I find it very difficult to use Meteor Stone effectively against Falcon, as he likes to recover very low with Falcon Dive.
Stage Picks
Avoid stages with vertical walls, as Falcon's vertical recovery is amazing if he has access to an easy wall jump. My preferred stages against Falcon are Battlefield (platforms make it more difficult for him to juggle effectively) and Halberd (sharking potential and low ceiling). I try to avoid Delfino Plaza because a lot of the transformations have really close side blast zones, and Falcon can get easy fthrow kills due to his sliding property on his dash-grab.
Additional Notes
Falcon has to play this matchup pretty intelligently to stand a chance.
Most Falcons are used to being able to rely on their dash grab/attack, which we can crouch under. Once they realize this, all the Falcons I've fought will try to wall me out with spaced bairs, since their approach game is pretty much destroyed by our crouch. Be smart, and get in when you can.
Utilt combos are devastating against Falcon, so try to get them when you can. Also, opt for horizonal kill options if possible. Falcon is pretty diffcult to kill vertically, and you can exploit his recovery even if you don't kill horizontally.
Offstage is where this matchup gets really exciting. Kirby's vertical and horizontal air speeds are pretty bad, so most Falcons will try to get either a bair stage spike or a dair on you if you're offstage and recovering low. If you have Upper Cutter, you can use it on reaction to punish this and maybe get a stage spike. If not, just try to air-dodge or have a tech ready. If Falcon is offstage, Kirby has SO MANY ways to kill him. If he recovers high - Jumping Inhale, fair, Upper Cutter, bair, or double-dair. If he recovers low - Falcon can mix up when he uses Falcon Dive, since it snaps to ledge at any point of the move. Try to wait for him to start Falcon Dive or get low enough to where he HAS to use it, then you can gimp him with practically any aerial (dair is preferred). Ledge trumps are also really easy to pull off against Falcon, especially with Upper Cutter - using Upper Cutter against a low-recovering Falcon is practically a guaranteed stage spike or ledge trump if you use it correctly.
Oh, and on the chance that Falcon starts comboing the **** out of you (which will likely happen at least once), returning to the ledge is your best bet. With Kirby's floaty-ness, Falcon can get easy uair juggles on him if you try to recover to mid-stage. If you think you can read what he's going for and airdodge appropriately, though, you can get a really nice dair to whatever you want as a great punish.
Overall Score
This matchup is
60:40
, in my opinion. Falcon has to generally put in a lot more effort than Kirby to get a comparable result, and Kirby absolutely wrecks Falcon offstage.
Note: This is only for customs on. I have no experience with customs off, but I can only assume that it would be cake for Falcon to edgeguard Kirby without Upper Cutter, probably making this matchup even or in Falcon's favor.